What is the Greatest Common Factor of 42000 and 42005?

Greatest common factor (GCF) of 42000 and 42005 is 5.

GCF(42000,42005) = 5

We will now calculate the prime factors of 42000 and 42005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42000 and 42005.

How to find the GCF of 42000 and 42005?

We will first find the prime factorization of 42000 and 42005. After we will calculate the factors of 42000 and 42005 and find the biggest common factor number .

Step-1: Prime Factorization of 42000

Prime factors of 42000 are 2, 3, 5, 7. Prime factorization of 42000 in exponential form is:

42000 = 2⁴ × 3¹ × 5³ × 7¹

Step-2: Prime Factorization of 42005

Prime factors of 42005 are 5, 31, 271. Prime factorization of 42005 in exponential form is:

42005 = 5¹ × 31¹ × 271¹

Step-3: Factors of 42000

List of positive integer factors of 42000 that divides 42000 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000

Step-4: Factors of 42005

List of positive integer factors of 42005 that divides 42000 without a remainder.

1, 5, 31, 155, 271, 1355, 8401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42000 and 42005. The biggest common factor number is the GCF number.
So the greatest common factor 42000 and 42005 is 5.

Also check out the Least Common Multiple of 42000 and 42005